Let's be fully specific; since we already have the term 'ping-pong' planets for ones that switch off between the two stars, how about 'ping planets' for ones orbiting the larger of the binary and 'pong planets' for ones orbiting the smaller?

(For the edge case where the two stars have exactly equal masses to the level of our ability to detect, 'pang planets' I guess.)

Yerushalmi wrote:I guess an intrabinary planet would be one where the suns pull on the planet equally so it doesn't move at all?

"Interbinary" seems to fit that situation, as the planet would always be between the two stars. (It doesn't exist of course, as it would be unstable.)

EngrBohn wrote:I suggest that "the other type" be called a Nightfall binary, after Asimov's story.

Lagash, the planet in Nightfall, has no less than six suns, so there should be plenty of chances to see rainbows.

Mikeski wrote:

speising wrote:I assume the "3" as radius in the picture should be "6".

Then his angle is wrong, too, since tan-1(0.5/3)x2 = 18.9o. (Calling that "about 18" is a bit odd, too, but unimportant given that we only care if it's greater or less than 84.)

Maybe the pic is correct and the previous text is wrong?

In the article that note 7 links to, the relevant results seem to be in table 7 on page 11. The numbers are described as "the critical semimajor axis in units of the binary semimajor axis", and range from 2.0 to 4.2. When the orbits are close enough to circular we can read "semimajor axis" as "radius". A mass ratio µ of 0.5 means that the suns have equal masses. For the easiest case, circular orbits (e = 0.0) and equal masses (µ = 0.5), the planet's critical distance from the center of the system (critical semimajor axis) is 2.3 times the suns' distance from the center of the system (binary semimajor axis) – not the suns' distance from each other. That means an angle of tan-1(1/2.3)·2 ≈ 47°.

Note also that in the article an orbit is considered stable if the planet survives for just a few thousand years, and there are regions further out that are unstable due to resonance. I find it doubtful that a planet can survive that close to a binary star long enough for beings who can look at rainbows to evolve.

A) It is possible to have more than half the circle of a rainbow above the horizon - the Earth's surface is not smooth, and human eyes are usually above ground level. When your eyes are higher than the horizon, and the sun's image is touching the horizon, the center of a rainbow will be above the horizon. In the case of standing near the top of a tall object, the center of a rainbow will be above the horizon for a much wider range of sun elevations. Also, Third and Fourth rainbows are centered on the sun's image, so when the sun is above the horizon, so are their centers.

B) In the final illustration, notwithstanding his earlier assertion, Randall has drawn one of the two rainbows with a center significantly above the horizon.

Well, mystery solved about that time I was sure I had seen a triple-rainbow, years ago. I hadn't seen primary, secondary and tertiary arcs, opposite the sun, I'd actually seen primary, quinary and secondary ones, instead. No, I didn't get a picture, sorry.

(Also, having just illustrated arcs number 3 and 4 in the sunward direction, he then says "Rainbows appear on the other side of the sky from the Sun", without specifying why he's ignoring those two at that point in the text. He then also neglects the usual caveat of rainbow-rings being visible from elevated (especially flying) viewpoints, strangely, given that this latter situation is most often noted whenever such a technical discussion is to be found. Strange. Probably details lost to editing, though.)

((semi-related ninjaing by rmsgrey, I note, whilst Previewing))

Talking of editing, ETAing because I forgot I was going to mention it... The Tatooine stars are of different spectra, so the bows should not be identical in colour-spread (at least in intensity).

Regardless of what the correct radius of the orbit should be, the current math is wrong. If the planet is 6 times further away than the two stars are from each other, then the angle is about 9.5 degrees (2 * tan^-1(0.5 * 1 / 6)). You split the sun-sun distance in half to get 2 right triangles, do the usual trigonometry, and then add the resulting angles up again.

Sometimes when the weather is right we can see a full circle rainbow by looking directly up at the sun (well, you know, in the direction of the sun-please don't try looking directly at the sun!) when it is covered by a certain kind of cloud. I remember someone saying that it is caused by a certain kind of ice formation in the atmosphere. I also heard that it is unique to the Inland Northwest (USA). From the diagram I guess this would be the "third" or "fourth" rainbow. Perhaps someone flying would be able to look down and see a circle or two below them if there were a solid background against which to see it.

In the literature, orbiting one star is an "s-type" (for "satellite-type") orbit, while orbiting both stars is a "p-type" (for "planetary-type") orbit. So a circumbinary planet is a p-type planet, while the other type is an s-type planet.

But that's maybe a little bit cryptic, and Randall might've been looking for a less jargony word.

Rombobjörn wrote:Note also that in the article an orbit is considered stable if the planet survives for just a few thousand years, and there are regions further out that are unstable due to resonance. I find it doubtful that a planet can survive that close to a binary star long enough for beings who can look at rainbows to evolve.

It all depends -- there's a rather unusual Tri-solar system where a couple of the planets lasted for millions of years. The system started out with quite a few planets, but one by one their orbits went unstable -- or to be exact, unable to avoid the suns -- and were lost to one sun or another.

cellocgw wrote:It all depends -- there's a rather unusual Tri-solar system where a couple of the planets lasted for millions of years. The system started out with quite a few planets, but one by one their orbits went unstable -- or to be exact, unable to avoid the suns -- and were lost to one sun or another.

After reading this What-If I'm left wondering what the hell it was I saw many years ago. There was an ordinary rainbow, then a second rainbow with reversed colours outside the first rainbow and almost as bright as it was, and then a third rainbow outside the second one with colours reversed again (so the same as an ordinary rainbow), very faint and flickering in and out of existence. I thought it was a third order rainbow but now I learned that those are supposed to be on the other side of the sky. It can't have been a fifth order rainbow, can it? What could it have been?

Priceguy wrote:After reading this What-If I'm left wondering what the hell it was I saw many years ago. There was an ordinary rainbow, then a second rainbow with reversed colours outside the first rainbow and almost as bright as it was, and then a third rainbow outside the second one with colours reversed again (so the same as an ordinary rainbow), very faint and flickering in and out of existence. I thought it was a third order rainbow but now I learned that those are supposed to be on the other side of the sky. It can't have been a fifth order rainbow, can it? What could it have been?

justbennett wrote:Sometimes when the weather is right we can see a full circle rainbow by looking directly up at the sun (well, you know, in the direction of the sun-please don't try looking directly at the sun!) when it is covered by a certain kind of cloud. I remember someone saying that it is caused by a certain kind of ice formation in the atmosphere. I also heard that it is unique to the Inland Northwest (USA). From the diagram I guess this would be the "third" or "fourth" rainbow. Perhaps someone flying would be able to look down and see a circle or two below them if there were a solid background against which to see it.

Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.---If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

Priceguy wrote:After reading this What-If I'm left wondering what the hell it was I saw many years ago. There was an ordinary rainbow, then a second rainbow with reversed colours outside the first rainbow and almost as bright as it was, and then a third rainbow outside the second one with colours reversed again (so the same as an ordinary rainbow), very faint and flickering in and out of existence. I thought it was a third order rainbow but now I learned that those are supposed to be on the other side of the sky. It can't have been a fifth order rainbow, can it? What could it have been?

Priceguy wrote:After reading this What-If I'm left wondering what the hell it was I saw many years ago. There was an ordinary rainbow, then a second rainbow with reversed colours outside the first rainbow and almost as bright as it was, and then a third rainbow outside the second one with colours reversed again (so the same as an ordinary rainbow), very faint and flickering in and out of existence. I thought it was a third order rainbow but now I learned that those are supposed to be on the other side of the sky. It can't have been a fifth order rainbow, can it? What could it have been?

Great. Now all we have to do is to get it to rain on Tatooine. In the Earthly Tataouine in Tunisia where that part of Star Wars was shot the annual rainfall averages 134 mm. This is nothing like as dry as the Atacama Desert in Chile, with an average rainfall of 15 mm per year. Some locations there average 1 mm of rain per year, and some weather stations in the region have never recorded any rain at all.

The brightness of the solar rainbow(s) have a hard time competing with the daylight sky. Any daytime lunar-rainbow would be dimmer still (you can see a part-lit1 moon against the daylight 'background', but it's nowhere near as blinding as the Sun) and intuition suggests that it wouldn't be easy to see, however bright you get it2.

There's probably been someone do this, but I suspect heavy preparation and post-processing, alike, were necessary.

1 The 'closer' the two bodies are, the thinner the Moon's crescent, the less light.2 The best daylight Moon is near-opposite (just day-side of dawn/dusk). And then the moonbow would be near to (and probably 'surround' !) the glaring Sun, making it more difficult to observe, and a fish-eye lens/composite-photo to get into a single pucture.

If there are an infinite number of arcs for every rainbow, just beyond third arc impossible to see with the naked eye, then really isn't there an infinite number of rainbow arcs naked to the eye anywhere we are standing at all times as long as there is moisture in the air?

Soupspoon wrote:Well, mystery solved about that time I was sure I had seen a triple-rainbow, years ago. I hadn't seen primary, secondary and tertiary arcs, opposite the sun, I'd actually seen primary, quinary and secondary ones, instead. No, I didn't get a picture, sorry.

(Also, having just illustrated arcs number 3 and 4 in the sunward direction, ...

Priceguy wrote:After reading this What-If I'm left wondering what the hell it was I saw many years ago. There was an ordinary rainbow, then a second rainbow with reversed colours outside the first rainbow and almost as bright as it was, and then a third rainbow outside the second one with colours reversed again (so the same as an ordinary rainbow), very faint and flickering in and out of existence. I thought it was a third order rainbow but now I learned that those are supposed to be on the other side of the sky. It can't have been a fifth order rainbow, can it? What could it have been?

I doubt that either of you saw I quinary or higher rainbow, they are just to faint to be seen with the naked eye; I won't say that some post-processing of a picture might be able to bring out a quinary bow. Priceguy, if you look at the diagram in the xkcd article you will notice that the fifth order bow is inbetween the primary and secondary, not outside the secondary. What both of you likely saw was a reflection bow caused by sunlight reflecting off a body of water behind you. In the diagram there, one can see that the top of the primary reflection bow can be above the secondary normal bow, at least most of the way down.

The mystery deepens rematerialises, then, for there was no body of water in my case.Within 100yds or so, I can even pinpoint where I was, to confirm my memories of the terrain, though it be a couple of decades ago... (53°13.7'N, 1°9.25'W) The time was probably around 7pm BST, but I can only guess 'maybe June?', if anyone wants the exact time of year.No matter. Mysteries are what makes life interesting. And money.

What if you include elliptical orbits? You could have the planet orbitting one star, but at times the stars are on the same side, and pretty close (I know, this does induce the very occasional huge giant pull of the star when occasionally the planet and outer star get close enough, if they do end up getting close enough that is).

There is probably about 10 binary star system setups I could come up with (and more for a trinary system, as you can have stars orbitting stars due to white dwarfs, brown dwarfs & neutron stars). The setups then get even more elaborate when you include non-circular orbits.

So it could be "the other kind of planet" on an elliptical orbit (or alternatively, if one of the stars is larger by a good amount, be orbitting the smaller star which would be orbitting the larger one to an extent, although I imagine to keep the brightness the same, it'd have to be something special about one of the stars age, composition or density, perhaps from it absorbing a neutron star).